"Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable" By Lars Ahlfors was very enjoyable to me. However, I read it after I already knew Complex Analysis.

i second tristan needham's visual complex analysis.

some other good ones:

* the one we used in my undergrad course was fisher's complex variables which is great if you're learning for the purposes of applications. it's a cheap dover book.

* rudin's real and complex analysis (if theory is your thing. note that rudin's books, while great, do require a good background in math).

* as the article mentions, eli stein has a series of books on the four main branches of analysis. i believe the second book is on complex analysis.

I've heard very good things about Visual Complex Analysis, as well.